The Algebra of Supernatural Matrices

The algebra of supernatural matrices is a key example in the theory of locally finite central simple algebras. Supernatural matrices are a minimal solution to the equation of unital algebras Mn(X) ∼= X, which we compare to several similar conditions involving cancellation of matrices. This algebra has appeared under various names before, and it generalizes both McCrimmon's deep matrices algebra and m-petal Leavitt path algebra.

Publication Details

Journal
The Mathematics Enthusiast
Published
2025-03-10
Primary Topic
Laser Design and Applications
Type
article
Field-Weighted Citation Impact
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article

The Algebra of Supernatural Matrices

The Mathematics Enthusiast
Laser Design and Applications
article

The Algebra of Supernatural Matrices

article en

Abstract

The algebra of supernatural matrices is a key example in the theory of locally finite central simple algebras. Supernatural matrices are a minimal solution to the equation of unital algebras Mn(X) ∼= X, which we compare to several similar conditions involving cancellation of matrices. This algebra has appeared under various names before, and it generalizes both McCrimmon's deep matrices algebra and m-petal Leavitt path algebra.

The Mathematics Enthusiast
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Laser Design and Applications
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The Algebra of Supernatural Matrices · The Mathematics Enthusiast (2025) | TGRS Research Map | TGRS